Nat. Hazards Earth Syst. Sci., 17, 305–314, 2017 www.nat-hazards-earth-syst-sci.net/17/305/2017/ doi:10.5194/nhess-17-305-2017 © Author(s) 2017. CC Attribution 3.0 License. Spatio-temporal modelling of lightning climatologies for complex terrain Thorsten Simon1,2, Nikolaus Umlauf2, Achim Zeileis2, Georg J. Mayr1, Wolfgang Schulz3, and Gerhard Diendorfer3 1Institute of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck, Austria 2Department of Statistics, University of Innsbruck, Innsbruck, Austria 3OVE-ALDIS, Vienna, Austria Correspondence to: Thorsten Simon ([email protected]) Received: 1 June 2016 – Discussion started: 4 July 2016 Revised: 16 January 2017 – Accepted: 8 February 2017 – Published: 6 March 2017 Abstract. This study develops methods for estimating light- 2000). Thus, the private and the insurance sector have a ning climatologies on the day−1 km−2 scale for regions with strong interest in reliable climatologies for such events, i.e. complex terrain and applies them to summertime observa- for risk assessment or as a benchmark forecast of a warning tions (2010–2015) of the lightning location system ALDIS system. in the Austrian state of Carinthia in the Eastern Alps. Lightning is a transient, high-current (typically tens of Generalized additive models (GAMs) are used to model kiloamperes) electric discharge in the air with a typical both the probability of occurrence and the intensity of light- length in kilometres. The lightning discharge in its entirety is ning. Additive effects are set up for altitude, day of the usually termed a lightning flash or just a flash. Each flash typ- year (season) and geographical location (longitude/latitude). ically contains several strokes , which are the basic elements The performance of the models is verified by 6-fold cross- of a lightning discharge (Rakov, 2016). Lightning flashes are validation. rare events. Around 0.5–4 km−2 yr−1 occur in the Austrian The altitude effect of the occurrence model suggests Alps (Schulz et al., 2005). Lightning location data that are higher probabilities of lightning for locations on higher el- homogeneously detected – with the same network and se- evations. The seasonal effect peaks in mid-July. The spatial lection algorithm – typically cover on the order of 10 years. effect models several local features, but there is a pronounced Consequently not enough data are available to compute a minimum in the north-west and a clear maximum in the east- spatially resolved climatology on the km−2 scale by simply ern part of Carinthia. The estimated effects of the intensity taking the mean of each cell – even less so if a finer temporal model reveal similar features, though they are not equal. The resolution than yr−1 is desired, which is the case for lighting main difference is that the spatial effect varies more strongly following a prominent annual cycle. Thus there is the need to than the analogous effect of the occurrence model. develop methods to robustly estimate lightning climatologies A major asset of the introduced method is that the resulting by exploiting information contained not only in each analy- climatological information varies smoothly over space, time sis cell and maybe its neighbouring cells but in the complete and altitude. Thus, the climatology is capable of serving as data set. Lightning might, e.g. depend on the altitude of the a useful tool in quantitative applications, i.e. risk assessment grid cells so that combining the information from all cells at and weather prediction. a particular altitude band increases the sample size and leads to a more robust estimate. Other common effects that might be exploited are geographical location, day of the year, time of day, slope orientation, distance from the nearest mountain 1 Introduction ridge, etc. One possibility of harnessing the complete data set to pro- Severe weather, associated with thunderstorms and lightning, duce a lightning climatology in such a manner is using gen- causes fatalities, injuries and financial losses (Curran et al., Published by Copernicus Publications on behalf of the European Geosciences Union. 306 T. Simon et al.: Spatio-temporal modelling of lightning climatologies eralized additive models (GAMs; see Hastie and Tibshirani, 2 Data 1990; Wood, 2006). They can include these common effects as additive terms. Each of these terms might be of arbitrary In this study 6 years of data (2010–2015) from the ALDIS complexity and represent the potentially non-linear relation- detection network (Schulz et al., 2005) are included. The data ship between lightning and the covariate. An additional ad- within this period are processed in real time by the same vantage of GAMs is the ability for inference. It can be tested lightning location algorithm ensuring stationarity with re- whether each of the included effects is actually an effect – or spect to data processing. The summer months May to Au- not significant and thus not exploiting common information gust are selected, as this is the dominant lightning season in the whole data set. GAMs allow the inclusion of expert in the Eastern Alps. The original ALDIS data contain sin- knowledge through the choice of the covariates. GAMs have gle strokes and information on which strokes belong to a been used to compile climatologies of extremes (Chavez- flash. In order to analyse flashes, only the very first stroke Demoulin and Davison, 2005; Yang et al., 2016) and full of a flash is taken into account. Both cloud-to-ground and precipitation distributions (Rust et al., 2013; Stauffer et al., intra-cloud lightning strikes are considered, as both typically 2016). A further benefit of GAMs is that all the parameters indicate thunderstorms which are of interest in this study. of a distribution, e.g. scale and shape, can be modelled and ALDIS is part of the European cooperation for light- not only the expected value (Stauffer et al., 2016). ning detection (EUCLID) (Pohjola and Mäkelä, 2013; Schulz In this study GAMs are applied to estimate a climatology et al., 2016), which bundles European efforts in lightning of the probability of lightning and a climatology of the ex- detection. Schulz et al.(2016) present an evaluation of the pected numbers of flashes with a spatial resolution of 1 km2 performance of lightning detection in Europe and the Alps and a temporal resolution of 1 day. They also serve as prox- by comparison against direct tower observations with respect ies for climatologies of the occurrence of thunderstorms (e.g. to detection efficiency, peak current estimation and location Gladich et al., 2011; Poelman, 2014; Mona et al., 2016) and accuracy. The median location error was found to be in the thunderstorm intensity. The climatologies will be compiled order of 100 m. Furthermore, they show that the flash detec- for a region in the south-eastern Alps. tion efficiency is greater than 96 % (100 %) if one of the re- A study investigating lightning data for the period 1992 turn strokes in a flash had a peak current greater than 2 kA to 2001 (Schulz et al., 2005) found that flash densities over (10 kA). However, it is impossible to determine the detec- the complex topography of Austria vary between 0.5 and tion efficiency of intra-cloud flashes without a locally in- 4 flashes km−2 yr−1 depending on the terrain. Data from the stalled very high frequency (VHF) network. Thus no attempt same lightning location system (LLS) were also analysed is made in Schulz et al.(2016) to characterize the detection to obtain thunderstorm tracks (Bertram and Mayr, 2004). efficiency of intra-cloud flashes. The key finding is that thunderstorms are often initialized at The region of interest is the state of Carinthia in the south mountains of moderate altitude and propagate towards flat of Austria at the border with Italy and Slovenia. Carinthia areas afterwards. extends 180 km in an east–west direction and 80 km in a Other studies focus on lightning detected in the vicinity of north–south direction. The elevation varies between 339 m the Alps: a 6-year analysis of lightning detection data over and 3798 m a.m.s.l. (above mean sea level). For invoking Germany reveals that the highest activity is in the north- elevation as a covariate into the statistical model (Sect.3) ern foothills of the Alps and during the summer months, digital elevation model (DEM) data (Kärnten, 2015), which when the number of thunderstorm days goes up to 7.5 yr−1 are on hand on a 10 m × 10 m resolution, are averaged over (Wapler, 2013). Lightning activity is also high along the 1 km × 1 km cells (Fig.1), which leads to a maximum eleva- southern rim of the Alps. Feudale et al.(2013) found ground tion of 3419 m a.m.s.l. with respect to this resolution. As the flash densities of up to 11 flashes km−2 yr−1 in north-eastern distribution of the altitude is highly skewed, the logarithm Italy, which is south of our region of interest, Carinthia. of the altitude serves as covariate, which is distributed more The paper is structured as follows: the lightning detection uniformly in the range 6 to 8. data, the region of interest, Carinthia, and the pre-processing The lightning data, for May to August of the 6 years, are of the data are described in Sect.2. The methods for estimat- transferred to the same 1 km × 1 km raster by counting the ing the lightning climatologies from the data are based on flashes within one spatial cell and per day. This procedure generalized additive models (Sect.3). The non-linear effects yields 9904 cells and 738 days for a total of n D 7 309 152 estimated for occurrence and intensity model and exemplary data points, from which 157 440 (2.15 %) show lightning ac- climatologies are presented afterwards (Sect.4).